Question: Luis is 2 times as old as Ashley. 30 years ago, Luis was 7 times as old as Ashley. How old is Ashley now?
Solution: We can use the given information to write down two equations that describe the ages of Luis and Ashley. Let Luis's current age be $l$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $l = 2a$ 30 years ago, Luis was $l - 30$ years old, and Ashley was $a - 30$ years old. The information in the second sentence can be expressed in the following equation: $l - 30 = 7(a - 30)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = 2a$ . Substituting this into our second equation, we get: $2a$ $-$ $30 = 7(a - 30)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $2 a - 30 = 7 a - 210$ Solving for $a$ , we get: $5 a = 180.$ $a = 36$.